I've been told that when applying for a teaching position, your reference letters can be written by anyone who is familiar with your teaching capabilities in detail. I feel that this primarily just means students, but I wonder if there's some unspoken rule that reference letters should come from people in positions of authority, e.g. professors for whom I've served as TA, administrative staff in the math department, etc. In reality, it's the students who know my teaching capabilities in detail, and perhaps to a lesser degree my friends, whereas professors and administrators have no direct knowledge my teaching abilities whatsoever, and might only have heard things here or there from students, or have read my student evaluations and seen the scores.

So should reference letters predominantly come from authority figures, or is it okay to have them all come from students?

If you're trying to get references from authority figures, it would be good for a letter to sound as if this figure was actually sitting in some of your classes. Then I presume that such a letter could be efficient.
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Leonid PetrovJul 9 '11 at 3:39

I voted to close; IMO 'career' questions are always a bit at the off/on-topic border for the site and getting more so [though I answered and argued in favor of some]. To me this one is 'across the border.'
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quidJul 9 '11 at 10:30

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@quid, MO is a great place for professional mathematicians to reach a wide audience of other professional mathematicians with questions relevant to professional mathematicians. When you have a math question, you could always just ask your colleagues, but often asking questions on MO proves to be very beneficial. The same goes for career-related questions. And it's not as though this site is, or ever will be, flooded with career questions.
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Amit Kumar GuptaJul 9 '11 at 17:52

Amit Kumar Gupta, what you say is in some sense certainly true. And, there are many discussions around this precise issue to be found on meta. What made me mainly vote to close is that the question has a still looser relation to (research) mathmatics than most other 'career' questions, many of which indeed got closed (without me contributing). In any case, I am glad you got useful answers, and good luck with your applications.
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quidJul 9 '11 at 18:30

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This question doesn't have mathematical criteria for determining correctness, so I've changed it to "Community Wiki" mode, which is better suited for making a sorted list of contributions.
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S. Carnahan♦Jul 10 '11 at 13:54

5 Answers
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IMO, The best teaching letters come from senior faculty members who have supervised you as a teacher and have sat in on several of your classes to observe your teaching. At many schools, it is standard procedure for this to happen. The letter should also discuss student evaluations, including numerical scores and some positive comments made by students on their evaluations. If this doesn't happen automatically at your school, then you should ask a faculty member to visit your class. This could be your advisor, or the faculty member in charge of the course you're teaching, or someone else on the faculty who you feel comfortable approaching. I would be very skeptical, for a variety of reasons, of an application whose only teaching letter(s) are from undergraduate(s). Indeed, any class is likely to contain at least a few students who are enthusiastic about the teacher, and a few who have a very negative opinion, so a couple of positive letters from handpicked student don't mean that much.

Thanks Joe. I'm choosing this as the correct answer since your suggestion that I ask some faculty to sit in on my lectures might help me correct the fact that currently no faculty are really familiar with my teaching.
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Amit Kumar GuptaJul 9 '11 at 17:59

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Yes, absolutely, if no faculty have seen you teach/TA, ask suitable people (very politely, because they are doing you a favor, etc) to please, please sit in... To echo other comments: the only "teaching letters" that have a positive impact are from relatively senior faculty who have seen your teaching. Many universities arrange for this to happen, but some don't, and the ones that do arrange it may not have the best people doing it! And, again, letters from students are generally considered throw-aways, at best, and at worst a sign of poor judgement on the applicant's part... Good luck!
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paul garrettJul 9 '11 at 19:35

Also, make sure that whoever is writing your teaching letter has access to your student evaluations. (But most likely, whoever is writing the letter has written a couple of them before, and will routinely get the evaluations in some way.)
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Arend BayerJul 10 '11 at 14:35

I wouldn't mind reading a letter from a student, but if the only letter covering teaching were from a student, it would definitely raise eyebrows.

It will also give someone on the committee an easy way to strongly object to you, and for most positions that's enough to bring an end to your hopes.

On a more philosophical note, your students are surely most familiar with your teaching, but they are not the best qualified to judge it. A student is likely unable to assess the depth of your knowledge, the ease of your course, or how you deal with problem students and complaints. All of these will be of supreme importance to the department looking to hire.

Thanks for your response! While you're right, students aren't qualified to judge my teaching skills, I doubt if the professors for whom I've TA'd would be qualified to do this either, simply because they have no experience of my teaching, how I deal with problem students, etc. Could a reference letter from a fellow TA/PhD student be appropriate?
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Amit Kumar GuptaJul 9 '11 at 17:56

"students not qualified to judge" is half-true, because after all, if they did not end up learning from the course, it is at least 50% a problem on the teacher's part. But otherwise, I agree with whatever else you have said above.
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SuvritJul 9 '11 at 18:44

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If you only have one, it should be from someone who would have suffered paperwork if a student had complained about you, and it should also be from somebody who has attended one of your classes, and it should also be from somebody who cares deeply about teaching. If there isn't somebody fitting all of that, you should create such a person. It's fair game to ask someone to attend a class and give you feedback, with the hidden agenda of later asking this person to write a letter.
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Kevin O'BryantJul 9 '11 at 19:37

@Kevin, thanks, that sounds like a great suggestion!
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Amit Kumar GuptaJul 10 '11 at 18:24

I agree with the previous answers but would put it more strongly. Your teaching letters should be only from people who not only know something about your teaching skills but who are experienced teachers themselves. A letter from a student is not appropriate. What is appropriate is to provide statistical data and maybe some comments (that are consistent with the statistical data) from teaching evaluations performed by the school or department.

You're a graduate student at Berkeley, and none of your professors can be bothered to observe you and evaluate your teaching skills? To be honest, I consider that to be a fundamental responsibility of a tenured faculty member. If you will be doing any more teaching before you apply for jobs, I encourage you to seek out an appropriate faculty member to observe and evaluate your teaching. Also, as I mentioned in my answer, you should definitely provide the results of student evaluations.
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Deane YangJul 9 '11 at 21:09

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Having just visited Berkeley for a semester, I can report that faculty there with TAs in their class are supposed to sit in on all of their TAs discussion sections at least once. In any event, I agree completely with Deane that it is a terrible idea to use a student's letter as your teaching letter for jobs. If you were applying for some teaching award, then a student's letter wouldn't look unusual, but in an academic job application-- at least for research department jobs -- it would be considered bizarre, almost like having a classmate write a research letter for you.
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KConradJul 9 '11 at 21:50

I agree with this strong statement. Another way to put it a bit simplified: If you are applying for a research job, then the teaching part of your application can only cost you a job, not gain you a job. Doing s.th. unusual there is pointless at best and risky at worst. If you are applying for a teaching job, then it is REALLY important that the information about your teaching is professional and informative.
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Arend BayerJul 10 '11 at 14:48

@KConrad, it's interesting you say that faculty are supposed to do this, in my four years of being a TA here I've only had one professor sit in once, and that was because it was my first semester teaching. @ABayer, it's not a research job, just a teaching job. @Deane, I don't think anyone said that faculty can't be bothered to observe me, but I'd have to ask someone to do it, it isn't something faculty would otherwise do.
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Amit Kumar GuptaJul 10 '11 at 18:22

Maybe a slightly different way to say what everyone else has is this: a letter from a student would not be seen as a letter of recommendation. Of course, it might literally be a letter which recommends you, but it simply wouldn't be seen as one. If you actually have a student who you think will write you a good letter, that would probably be nice supplementary material for your application, but it shouldn't be included in the list of letters on, say, mathjobs.

This is a slightly different response as most people are assuming you are intending to teach at the university level. I respond only for informational purposes for those teaching not at the university level.

As an undergraduate, I took an "advanced" math course with a Ph.D graduate student as the teacher. After finishing his degree, he ended up seeking prep school and community college positions out of interest to teach small groups of students. Not only did these schools ask for "authoritative" recommendations, but a number also asked for multiple student recommendations.

Admittedly, I was asked to write one -- I do not think I really had the perspective then, nor now, to write something. But it seems these less than university positions desire that additional information.